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Bulletin of the London Mathematical Society, 1998
Let \(A\) be a group of automorphisms of the finite group \(G\) such that \((|A|,|G|)=1\). The authors prove that \(|A|0\), groups \(G\) and \(A\leq\Aut(G)\) can be found such that \((|A|,|G|)=1\) and \(|A|>|G|^{2-\varepsilon}\). Furthermore, if \(A\) is nilpotent of class at most 2, then \(|A|
Pálfy, P. P., Pyber, L.
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Half-Transitive Automorphism Groups

Canadian Journal of Mathematics, 1966
Let G be a finite group and A a group of automorphisms of G. Clearly A acts as a permutation group on G#, the set of non-identity elements of G. We assume that this permutation representation is half transitive, that is all the orbits have the same size. A special case of this occurs when A acts fixed point free on G.
Isaacs, I. M., Passman, D. S.
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Automorphisms of Metabelian Groups

Canadian Mathematical Bulletin, 1998
AbstractWe investigate the problem of determining when IA(Fn(AmA)) is finitely generated for all n and m, with n ≥ 2 and m ≠ 1. If m is a nonsquare free integer then IA(Fn(AmA)) is not finitely generated for all n and if m is a square free integer then IA(Fn(AmA)) is finitely generated for all n, with n ≠ 3, and IA(F3(AmA)) is not finitely generated ...
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Automorphism groups ofFC-groups